# How do I find an interest rate using the formula a=p(1+r)^t?

Sep 15, 2014

To find the interest rate (r) in the formula $a = p {\left(1 + r\right)}^{t}$, you need to know the values of a (amount), p (principal) and t (time). You would take a and divide it by p. You will then take that result and take the t root of it. You then subtract that answer by 1 to get your interest rate in decimal form.

Here is an example:

You need to find the interest rate of an account that grew from $4000 to$4063 in 2 years.

$a = 4063$

$p = 4000$

$t = 2$

$4063 = 4000 {\left(1 + r\right)}^{2}$

$\frac{4063}{4000} = {\left(1 + r\right)}^{2}$

$1.01575 = {\left(1 + r\right)}^{2}$

$\sqrt{1.01575} = \sqrt{{\left(1 + r\right)}^{2}}$

$1.007844 = 1 + r$

$1.007844 - 1 = r$

$.007844 = r$

interest rate rounds to  .784 %